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Three-dimensional finite element simulations of ferroelectric polycrystals under electrical and mechanical loading. (English) Zbl 1171.74344

Summary: Complex, non-linear, irreversible, hysteretic behavior of polycrystalline ferroelectric materials under a combined electro-mechanical loading is a result of domain wall motion, causing simultaneous expansion and contraction of unlike domains, grain sub-divisions that have distinct spontaneous polarization and strain. In this paper, a 3-dimensional finite element method is used to simulate such a polycrystalline ferroelectric under electrical and mechanical loading. A constitutive law due to J. E. Huber, N. A. Fleck, C. M.Landis and R. M. McMeeking [J. Mech. Phys. Solids 47, No. 8, 1663–1697 (1999; Zbl 0973.74026)] for switching by domain wall motion in multidomain ferroelectric single crystals is employed in our model to represent each grain, and the finite element method is used to solve the governing conditions of mechanical equilibrium and Gauss’s law. The results provide the average behavior for the polycrystalline ceramic. We compare the outcomes predicted by this model with the available experimental data for various electromechanical loading conditions. The qualitative features of ferroelectric switching are predicted well, including hysteresis and butterfly loops, the effect on them of mechanical compression, and the response of the polycrystal to non-proportional electrical loading.

MSC:

74F15 Electromagnetic effects in solid mechanics
74E15 Crystalline structure
74S05 Finite element methods applied to problems in solid mechanics

Citations:

Zbl 0973.74026
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References:

[1] Arlt, G., The influence of microstructure on the properties of ferroelectric ceramics, Ferroelectrics, 104, 217-227 (1990)
[2] Cocks, A. C.F.; McMeeking, R. M., A phenomenological constitutive law for the behavior of ferroelectric ceramics, Ferroelectrics, 228, 219-228 (1999)
[3] Cook, R. D.; Malkus, D. S.; Plesha, M. E.; Witt, R. J., Concepts and Application of Finite Element Analysis (2002), Wiley: Wiley New York
[4] Elhadrouz, M.; Ben Zineb, T.; Patoor, E., Constitutive law for ferroelastic and ferroelectric piezoceramics, J. Intell. Mater. Syst. Struct., 16, 221-236 (2005)
[5] Fang, D.; Li, C., Nonlinear electric-mechanical behavior of a soft PZT-51 ferroelectric ceramic, J. Mater. Sci., 34, 4001-4010 (1999)
[6] Fett, T.; Müller, S.; Munz, D.; Thun, G., Nonsymmetry in the deformation behavior of PZT, J. Mater. Sci. Lett., 17, 261-265 (1998)
[7] Haug, A.; Huber, J. E.; Onck, P. R.; Van der Giessen, E., Multi-grain analysis versus self-consistent estimates of ferroelectric polycrystals, J. Mech. Phys. Solids, 55, 648-665 (2007) · Zbl 1173.74012
[8] Huber, J. E.; Fleck, N. A., Multi-axial electrical switching of a ferroelectric: theory versus experiment, J. Mech. Phys. Solids, 49, 785-811 (2001) · Zbl 1021.74013
[9] Huber, J. E.; Fleck, N. A.; Landis, C. M.; McMeeking, R. M., A constitutive model for ferroelectric polycrystals, J. Mech. Phys. Solids, 47, 1663-1697 (1999) · Zbl 0973.74026
[10] Hwang, S. C.; McMeeking, R. M., A finite element model of ferroelastic polycrystals, Int. J. Solids Struct., 36, 1541-1556 (1999) · Zbl 0958.74065
[11] Hwang, S. C.; Lynch, C. S.; McMeeking, R. M., Ferroelectric/ferroelastic interactions and a polarization switching model, Acta Metal. Mater., 43, 2073-2084 (1995)
[12] Hwang, S. C.; Huber, J. E.; McMeeking, R. M.; Fleck, N. A., The simulation of switching in polycrystalline ferroelectric ceramics, J. Appl. Phys., 84, 1530-1540 (1998)
[13] Jaffe, B.; Cook, W. R.; Jaffe, H., Piezoelectric Ceramics (1971), Academic Press: Academic Press London and New York
[14] Kamlah, M.; Jiang, Q., A constitutive model for ferroelectric PZT ceramics under uni-axial loading, Smart Mater. Struct., 8, 441-459 (1999)
[15] Kamlah, M.; Tsakmakis, C., Phenomenological modeling of the non-linear electromechanical coupling in ferroelectrics, Int. J. Solids Struct., 36, 669-695 (1999) · Zbl 0973.74544
[16] Kamlah, M.; Liskowsky, A. C.; McMeeking, R. M.; Balke, H., Finite element simulation of a polycrystalline ferroelectric based on a multidomain single crystal switching model, Int. J. Solids Struct., 42, 2949-2964 (2005) · Zbl 1093.74564
[17] Kessler, H.; Balke, H., On the local and average energy release in polarization switching phenomena, J. Mech. Phys. Solids, 49, 953-978 (2001) · Zbl 0980.74020
[18] Landis, C. M., Fully coupled, multi-axial, symmetric constitutive laws for polycrystalline ferroelectric ceramics, J. Mech. Phys. Solids, 50, 127-152 (2002) · Zbl 1023.74016
[19] Landis, C. M., On the strain saturation conditions for polycrystalline ferroelastic materials, J. Appl. Mech., 70, 470-478 (2003) · Zbl 1110.74529
[20] Lines, M. E.; Glass, A. M., Principles and Applications of Ferroelectrics and Related Materials (1977), Oxford University Press: Oxford University Press Oxford
[21] Lynch, C. S., The effect of uniaxial stress on the electro-mechanical response of 8/65/35 PLZT, Acta Mater., 44, 4137 (1996)
[22] Lynch, C. S., On the development of multiaxial phenomenological constitutive laws for ferroelectric ceramics, J. Intell. Mater. Syst. Struct., 9, 555-563 (1998)
[23] McMeeking, R. M.; Landis, C. M., A phenomenological multi-axial constitutive law for switching in polycrystalline ferroelectric ceramics, Int. J. Eng. Sci., 40, 1553-1577 (2002) · Zbl 1211.74100
[24] Michelitsch, T.; Kreher, W., A simple model for the nonlinear material behavior of ferroelectrics, Acta Mater., 46, 5085-5094 (1998)
[25] Peirce, D.; Shih, C. F.; Needleman, A., A tangent modulus method for rate dependent solids, Comput. Struct., 18, 875-887 (1984) · Zbl 0531.73057
[26] Steinkopff, T., Finite-element modeling of ferroic domain switching in piezoelectric ceramics, J. Eur. Ceram. Soc., 19, 1247-1249 (1999)
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